\documentclass[border=2mm]{standalone}
\usepackage{pgfplots}
\usepackage{amsmath}
\usepackage[scaled]{helvet}
\usepackage[T1]{fontenc}
\renewcommand\familydefault{\sfdefault}
\usepackage[eulergreek]{sansmath}
\pgfplotsset{
tick label style = {font=\sansmath\sffamily}}

\pgfkeys{/pgf/number format/fixed, /pgf/number format/precision=5, /pgf/number format/.cd, 1000 sep = {}}
\pgfplotsset{compat=newest}

\begin{document}

\pgfmathdeclarefunction{gauss}{2}{\pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
}
\begin{tikzpicture}

\begin{axis}[
    width=10cm, % Set the width of the axis
    height=6cm, % Set the height of the axis
    scaled ticks=false,
    axis lines=center,
    enlargelimits=upper,
    line width=0.8,
    xlabel = {$x$},
    ylabel = {$f(x)$}, 
    yticklabel = \empty,
    xmin = -5, xmax = 4.5,
    ymin = -0.05, ymax = 0.45,
    every axis x label/.style={at={(ticklabel* cs:1.02)}, anchor=west,}, every axis y label/.style={at={(ticklabel* cs:1.02)}, anchor=south}
]

    \begin{scope}
        \clip (1.96,0) rectangle (4,1);
        \fill[red!40, opacity=0.6] plot[domain=-4:4, smooth] (\x, {1/sqrt(2*pi)*exp(-\x*\x/2)}) -- (4, 0) -- (-4, 0) -- cycle;
    \end{scope}

    \begin{scope}
        \clip (-1.96,0) rectangle (-4,1);
        \fill[red!40, opacity=0.6] plot[domain=-4:4, smooth] (\x, {1/sqrt(2*pi)*exp(-\x*\x/2)}) -- (-4, 0) -- (4, 0) -- cycle;
    \end{scope}

\addplot + [smooth, mark=none, domain=-4:4, samples=100, color=red, line width=1.5] {gauss(0,1)};

\node at (-2.8,0.3) {\color{red!90!black}$f(x)=\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}x^2}$};

\node at (3,0.45) {\small\color{gray}$95\%$ confidence interval};

\node at (3,0.35) {\small\color{gray}$\mu\pm \underbrace{1.96}_{\text{two-tailed}}\sigma$};

\draw[arrows=<-, thick, color=red!70] (1.96,0.02)--(1.96,0.13);
\node at (2,0.16) {\footnotesize\color{red!90!black}$1.96$};

\draw[arrows=<-, thick, color=red!70] (2.2,0.015)--(3,0.075);
\node at (3.4,0.1) {\footnotesize\color{red!90!black}Area = $0.025$};

\node at (-0.5,0.4) {0.4};

\end{axis}
\end{tikzpicture}

\end{document}